
The Argentine put aside his first-round defeat this week in Basle to lift his game on the big occasion, saving ten of the dozen break points he faced.
Nalbandian won into the second round against Spain's veteran Carlos Moya.
In the only other main draw match of an event which began a day early in hopes of a box office bonanza, Frenchman Gilles Simon did the home crowd proud as he put out Italian Potito Starace 6-3, 3-6, 6-3.
Nalbandian won his first set over Almagro in 41 minutes of patient play, then rode a break in the seventh game to victory in less than 90 minutes.
The winner of the Moya clash is likely to face top seed Roger Federer, playing Paris for the first time since 2003.
The Swiss is fresh from a second straight home title at the Swiss Indoors Sunday, but said he is determined to play at the Bercy arena after missing the event last year.
Organisers are relieved after only one later pullout damaged their draw - with Andy Roddick withdrawing hurt.
The American has already qualified for the November 11-18 season-wrapup Masters Cup in Shanghai.
Two remaining spots in the field will be decided this week in Paris, with Scot Andy Murray rising into 11th place for the eight-man short-list by virtue of his St Petersburg title on Sunday.
Six players have already qualified for the season finale but up to 20 could be struggling in Paris to nail down one of the two open spots.
Spain's Rafael Nadal, still troubled by knee tendinitis, will be making his Paris debut after losing in his only qualifying match four years ago. The world number two opens after a bye against the winner from Jurgen Melzer and Filippo Volandri.